How does earth's orbit around the sun change over time?
The main change of the Earth's orbit over time is that perihelion precesses. Perihelion is currently around 3 January. It is getting progressively later by about one day every 70 years due to precession.
In fact the Earth's orbit is constantly changing due to the gravitational pull of the Sun, Moon and other planets. One impact of this is that perihelion can be any time between 2 and 4 January.